The z-score follows a normal distribution, which is known as the standard normal distribution
The standard normal distribution, also known as the Z-distribution or the standard normal curve, is a probability distribution that is commonly used in statistics
The standard normal distribution, also known as the Z-distribution or the standard normal curve, is a probability distribution that is commonly used in statistics. It is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. The z-score is a measure of how many standard deviations a given value is from the mean.
To find the z-score for a particular value in a normal distribution, you can use the formula:
z = (x – μ) / σ
Where:
– z is the z-score
– x is the value you are interested in
– μ is the mean of the population or distribution
– σ is the standard deviation of the population or distribution
For example, let’s say we have a normally distributed population of test scores with a mean of 75 and a standard deviation of 10. If we want to find the z-score for a test score of 85, we can plug the values into the formula:
z = (85 – 75) / 10
z = 10 / 10
z = 1
This means that a test score of 85 is 1 standard deviation above the mean. Positive z-scores indicate values above the mean, while negative z-scores indicate values below the mean.
The standard normal distribution is useful because it allows us to compare values from different normal distributions and determine how unusual or typical a value is relative to a particular population. By converting values to z-scores, we can calculate probabilities, determine percentiles, and perform other statistical analyses.
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